After California schools eliminated art programs and increased class sizes to survive budget cuts, they are finally on the verge of getting more money thanks to voter-approved taxes and economic recovery.

But K-12 districts may not share equally in the expanding budget pie.

Gov. Jerry Brown is pushing hard to overhaul California’s convoluted school funding system. His plan has two major objectives: Give K-12 districts greater control over how they spend money, and send more dollars to impoverished students and English learners.

Studies show that such children require more public help to reach the same level of achievement as their well-off peers. But as rich and poor communities alike clamor for money in the wake of funding cuts, Brown’s plan could leave wealthy suburbs with fewer new dollars than poorer urban and rural districts.

That makes perfect sense, said Michael W. Kirst, president of the State Board of Education and a Stanford University professor who co-wrote a 2008 paper that became the model for Brown’s proposal.

“Low-income people have less resources to invest in their children,” Kirst said. “A lot of investment comes from parental ability to buy external things for their kids that provide a better education. In the case of low-income groups, they can’t buy tutors, after-school programs or summer experiences.”

The Democratic governor wanted to install his plan as part of the last budget, but changes were so dramatic that education interests balked. Brown is reworking his proposal for his January budget, hoping that passage of his tax hike has given school officials confidence they will all receive sufficient money.

Brown officials held three workshops this fall to solicit input, as well as build good will with education groups.

One example from the Sacramento region shows how Brown’s proposal would shift dollars to students in need.

In Brown’s last proposal, Buckeye Union School District in affluent El Dorado Hills and neighboring communities would receive $7,757 per student in 2018-19, according to analysis by the Public Policy Institute of California. Robla Elementary School District in working-class North Sacramento would get $10,554 per student.